Why are lines AC and RS skew lines?

Answer:

3/5

Step-by-step explanation:

\( \frac{27}{45} = \frac{27 \div 9}{45 \div 9} = \frac{3}{5} \\ \)

Answer: What is the least number of gumballs jack has to buy to be certain he gets 6 gumballs of the same color?

Step-by-step explanation:

To be certain he gets 6 gumballs of the same color, Jack must buy at least 16 gumballs.

This is because he could buy 5 gumballs of each color (for a total of 15 gumballs) and still not have 6 gumballs of the same color. However, if he buys one more gumball, he will have at least 6 gumballs of one color.

Therefore, the least number of gumballs Jack has to buy to be certain he gets 6 gumballs of the same color is 16.

{Hope This Helps! :)}

Answer: D

Step-by-step explanation:

      This 275 is a constant variable, meaning that the variable (in this case, w of weeks) won't change it. This means there was already 275 gallons in the tank, and was not added during the first week.

      This means the 275 in the equation represents the amount of water, in gallons, in the tank currently.

Answer:

24

Step-by-step explanation:

The total number of students in the three sections is 36 + 40 + 48 = 124.

To find the maximum number of students in each row, we need to divide the total number of students by the number of rows, rounded down to the nearest integer.

Let's call the maximum number of students in each row "x". Then, we can write the equation:

x * n = 124

To find the maximum value of x, we need to find the maximum value of n such that the result of x * n is less than or equal to 124.

Starting with n = 1, we can increment n and calculate x for each value of n until x * n is greater than 124.

For n = 1, x * n = 124, so x = 124.

For n = 2, x * n = 62, so x = 62.

For n = 3, x * n = 41, so x = 41.

For n = 4, x * n = 31, so x = 31.

For n = 5, x * n = 24.8, which is not an integer, so we round down to 24.

Therefore, the maximum number of students in each row is 24, with a total of 5 rows.

Answer:

Step-by-step explanation:

Let's call the maximum number of students in each row "r". To find this value, we need to divide the total number of students by the number of rows. To ensure that all the students can fit into the rows, the number of students in each section must be divisible by the number of rows.

First, we find the least common multiple (LCM) of the number of students in each section, which will be the total number of students if we arrange them in the same number of rows. The LCM of 36, 40, and 48 is 240.

Next, we divide the LCM by the number of students in each section to find the number of rows:

r = LCM / 36 = 240 / 36= 6.67 (rounded down to 6)

So, the maximum number of students that can be in each row is 24

Yes , it is possible that t for every positive integer n there is a circle in the plane which contains exactly n lattice points in its interior

A lattice point may be defined as the point of intersection of two grid lines or more than two grid lines that is placed in a regularly spaced points arrays. This is called a lattice point.

A formal power series that encodes the coefficients of a sequence of numbers is a generating function.

Here, the coefficients of the sequence {Sₙ} are encoded by the generating function S(x). where Sₙ is the number of lattice paths as described above.

Here we will use the fact that the generating function for a sequence satisfies a functional equation that relates the generating function to the sequence itself to prove that 1 + (x – 1)S(x) + xS(x)² = 0,

Here, the functional equation is

S(x) = 1 + xS(x) + xS(x)²

This equation implies that

The term 1 on the right-hand side corresponds to the fact that to reach the point (0,0) (the starting point), there is exactly one way which is to stay at the starting point.

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Answer:

The first one

Step-by-step explanation:

1/5 =0.20

0.20 * 4 = 0.8 feet

0.20 * 6 = 1.2 feet

The mean of the decrease in rounded percentage of home is 7.14 which would used as misleading the about  data as raw data very far away from 7.14.

As given in the question,

Given rounded percentage decrease in home price is:

3, 3, 5, 6, 7, 7, 19

Mean of the rounded percentage

= ( Sum of all the values)/ (Number of values)

= ( 3 + 3 + 5 + 6 + 7 + 7 + 19) / 7

= 50 /7

=7.1428

= 7.14

7.14 is very far away from 3 and 19.

Mean is not representing  the correct information of the home price.

Using mean is misleading the correct information about percentage decrease.

Therefore, value of the mean is equal to 7.14 which mislead the decrease percentage.

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Answer:

so the length of square b is 50%.

The part in the steering column that allows for changes in the angle between the upper and lower shafts is the universal joint.

The universal joint, also known as a U-joint or Cardan joint, is a mechanical device that enables changes in the angle between two shafts that are not in a straight line. In the context of a steering column, the upper and lower shafts are connected by a universal joint.

As the steering wheel is turned, it exerts rotational force on the upper shaft of the steering column. The universal joint allows for the transmission of this rotational motion while accommodating changes in the angle between the upper and lower shafts. It provides flexibility and compensates for any misalignment between the two shafts, ensuring smooth and continuous rotation of the steering column.

The universal joint typically consists of two yokes connected by a cross-shaped component with needle bearings. These bearings allow for rotation in multiple axes, allowing the steering column to handle variations in the angle between the upper and lower shafts during steering movements.

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Answer:

Step-by-step explanation:

A triangle has 180 degrees in total. One of the angles are 145 degrees, so we can subtract and get 35 degrees. Then, it says that the remaining angles are in a ratio 2:3. So, we would have:

\(2x:3x = 35 \\2x+3x = 35\\5x=35\\x=7\)

Now that we know what x is, we can multiply that to our ratio:

\(2\cdot7=14 \text{ degrees for the first angle}\\3\cdot7=21 \text{ degrees for the second angle }\)

Answer:

y = 4x + 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x + 7 ← is in slope- intercept form

with slope m = 4

• Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation

to find c substitute (- 3, 2 ) into the partial equation

2 = - 12 + c ⇒ c = 2 + 12 = 14

y = 4x + 14 ← equation of parallel line

Answer:

\(\boldsymbol{y=4x+14}\)

Step-by-step explanation:

Hi student! Let me help you out on this question.

________

- - - - - - - - - - - - - - - - -

                                             ↪

First of all we need to find, the slope of the line that is parallel to the line \(\boldsymbol{y=4x+7}\). Which is pretty easy, considering the fact that the slopes of parallel lines are the same.

The slope of the line \(\boldsymbol{y=4x+7}\) is \(\boldsymbol 4\).

Which means the slope of the line that is parallel to the one above is also 4.

- - - - - - - - - - - - - - - - -

                                                 ↪

Now we should find the equation of the line. We know that its slope is 4, so let's stick in 4 for the slope into the slope-intercept form equation:

(remember, m denotes the slope and b denotes the y intercept).

\(\boldsymbol{y=mx+b}\)

Stick in 4 for the slope.

\(\boldsymbol{y=4x+b}\)

Note that we are also given a point that's on the line.

We can stick in its y-co-ordinate, 2. for y.

\(\boldsymbol{2=4x+b}\)

Now let's stick in -3 for x.

\(\boldsymbol{2=4(-3)+b}\)

Solve for b.

\(\boldsymbol{2=-12+b}\)

Add 12 to both sides.

\(\boldsymbol{2+12=b}\)

\(\boldsymbol{14=b}\)

                                               ↪

Now that we know the y-intercept, let's stick it into the slope-intercept form equation for b:

\(\boldsymbol{y=4x+14}\). Which is our final answer, the equation.

⇨Hope that this helped you out! Have a nice day ahead.⇦

Best Wishes!

\(\star\bigstar\boldsymbol{Reach\:far.\:Aim\:high.\:Dream \ big.}}\bigstar\star\)

◆◈-Greetings!-◆◈

- - - - - - - - - - - - - - - - - -

_____________

Answer:

1, 2 or 3 hours

Step-by-step explanation:

The inequality would be $20+$8x ≤ 50

$20 deposit plus $8 per hour times the # hours so you don't go over $50 so x could be 1,2,or 3 hrs.

Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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Answer:

We have 2 rational solutions

0 irrational solutions

0 complex solutions

Step-by-step explanation:

a^2 + 8a + 12 = 0

Using the discriminant

b^2 -4ac where ax^2 + bx+ c

so a =1  b = 8 and c = 12

8^2 -4(1)*12

64 - 48

16

Since the discriminant is greater than 0, we have 2 real solutions

since we can take the square root of 16, we have rational solutions

We have 2 rational solutions

Since this is a quadratic equations, there are only 2 solutions so there are

0 irrational solutions

0 complex solutions

Answer:

2 Rational Solutions

0 Irrational Solutions

0 Complex Solutions

Step-by-step explanation:

The discriminant of the quadratic formula is the name given to the portion underneath the radical (or the square root)"

\(x = \frac{1}{2} (-b\frac{ + }{ - } \sqrt{ {b}^{2} - 4ac })\)

Discriminant = D = b²-4ac

If D is less than 0 you have two complex solutions.

If D is equal to 0 you'll have one real solution.

If D is bigger than 0 you'll get two real solutions.

So here we have:

a=1

b=8

c=12

Which means D=64-4(1)(12)=64-48=16>0

D is bigger than 0, so you'll have two real solutions. And since 16 is a perfect square, they'll both be rational numbers.

Answer:

Y= x+1

Step-by-step explanation:

m=2-1/ 1-0; m=1

Y-2= 1(x-1)

Y= x-1+2

Y= x+1

1.3338 is the likelihood, The probability of anything occurring is known as probability.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

Explanation:

Mean (m) = 25

The standard deviation is 13

Sample size (n) is 95.

Chance that x will fall between 22 and 27.

Zscore = x - mean / s / n

If x = 22, Zscore is equal to (22 - 25) / (13/95).

For x = 27, Zscore is equal to (27 - 25) / (13/95) / n = 13 / 95, which is 1.3338.

1.3338 is the likelihood.

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T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).

To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.

For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).

As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).

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To solve the problem, let's go step by step.

1) Draw the K-map and find all prime implicants:

The given function f has 4 variables (d, c, b, a). So, we need to draw a 4-variable Karnaugh map (K-map). The K-map will have 2^4 = 16 cells.

The K-map for f is as follows:

```

        cd

ab     00 01 11 10

00 |   1   2   8   7

01 |   3   4   12 15

11 |   X   5   X   14

10 |   X   9   X   10

```

Now, let's find all the prime implicants:

- A: Group (1, 2, 3, 4) with d = 0.

- B: Group (2, 3, 7, 8) with b = 0.

- C: Group (3, 4, 12, 15) with a = 0.

- D: Group (2, 3, 4, 5) with c = 1.

- E: Group (7, 8, 14, 15) with b = 1.

- F: Group (4, 5, 9, 10) with a = 1.

- G: Group (8, 9, 12, 15) with c = 0.

- H: Group (12, 14, 15, 10) with d = 1.

2) Minimize f:

To minimize f, we need to simplify it by combining the prime implicants.

The minimized form of f can be expressed as the sum of prime implicants A, B, D, and E:

f = A + B + D + E

This can be further simplified, if desired, using Boolean algebra techniques.

Note: Please double-check the given function f and the tabulation method steps to ensure accuracy in the K-map and prime implicant identification.

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Answer:

49

Step-by-step explanation:

A= a^2 = 7^2 =49

The domain and the range of the graphare

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is a quadratic function

The rule of an quadratic function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -2

So, the range is y > -2

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Answer:

936 square units.

Step-by-step explanation:

Area formula of trapezoid: \(A=\frac{a+b}{2}h\)

given information:

   a = 40

   b = 64

   h = 18

plug them into the formula:

\(A=\frac{40+64}{2}\cdot 18\)

\(A = 936\)

Answer:

\(x=8\)

Step-by-step explanation:

\(x+9=17\\ x=17-9\\ x=8\)

Answer:

a) -0.4.

Step-by-step explanation:

2.6 + (-3)

= 2.6 - 3

= -0.4.

Answer: She walks at 3 miles per hour, and runs at 7 miles per hour.

Step-by-step explanation:

Let's define:

R = running rate

W = walking rate

We know that:

R = W + 4mi/h

and:

"She can run 21 miles in the same amount of time it takes her to walk 9 miles."

Here we can remember the relation:

Distance = time*speed

The above sentence says that, for a given time T, we have:

21mi = T*R

9mi = T*W

Then we have a system of 3 equations:

R = W + 4mi/h

21mi = T*R

9mi = T*W

To solve this, we could start by isolating T in one of the equations, let's do it in the last one:

9mi/W = T

Now we can replace that in the second one to get

21mi = 9mi*(R/W)

In this equation we could isolate R to get:

R = (21mi/9mi)*W = (7/3)*W

Now we can replace that in the first equation:

R = W + 4mi/h

(7/3)*W = W + 4 mi/h

And now we can solve this for W.

(7/3)*W - W = 4mi/h

(4/3)*W = 4mi/h

W = (3/4)*4mi/h = 3mi/h

And we could use also the first equation to find the running rate:

R = W + 4mi/h = 3mi/h + 4mi/h = 7mi/h

Then:

She walks at 3 miles per hour, and runs at 7 miles per hour.

Answer:

ggggg

Step-by-step explanation:

gfv

The volume of the sports drink that they have with them, in whole liters is: d. 30 liters

The volume of a rectangular shape, just like the rectangular block in the given problem, can be calculated using the formula:

Volume = (length)(width)(height).

From the information given, the rectangular block's dimensions are:]

Volume of one rectangular block = (6.0)(4.0)(10.5)

Volume of one rectangular block = 252 cm³

Convert 252 cm³ to liters:

1,000 cm³ = 1 liters

252 cm³ = 252/1,000 = 0.252 liters

120 packs of 0.252 liters = 120 × 0.252

= 30.24 ≈ 30 liters

Therefore, the volume of the sports drink that they have with them, in whole liters is: d. 30 liters

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The change-of-coordinates matrix from B to C is TBC=[13−12−54] and from C to B is TCB=[−1−24−3].

Why the change-of-coordinates matrix from B to C is TBC=[13−12−54] and from C to B is TCB=[−1−24−3]?

To find the change-of-coordinates matrix from B to C, we use the following formula:

TBC=[c1c2]B

where TBC is the change-of-coordinates matrix from B to C, and [c1 c2]B is the matrix whose columns are the coordinate vectors of c1 and c2 expressed as column vectors with respect to the basis B.

Now we have the following coordinates of c1 and c2 relative to B:So we have:

Thus,TBC=[c1c2]B=[2334][11 12]=[13−12−54]

Now to find the change-of-coordinates matrix from C to B, we use the following formula:

TCB=[b1b2]C

where TCB is the change-of-coordinates matrix from C to B, and [b1 b2]C is the matrix whose columns are the coordinate vectors of b1 and b2 expressed as column vectors with respect to the basis C.

Now we have the following coordinates of b1 and b2 relative to C:So we have:

Thus,TCB=[b1b2]C=[1122][23 34]=[−1−24−3]

Therefore, the change-of-coordinates matrix from B to C is TBC=[13−12−54] and from C to B is TCB=[−1−24−3].

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The change-of-coordinates matrix from B to C is [ -1/5 2/5 ][ 6/5 -1/5 ]  and then from C to B is [ 7/5 -2/5 ] [-2 1 ]

To find the change-of-coordinates matrix from B to C, we need to express the basis vectors of B in terms of the basis vectors of C and form the resulting matrix.

First, we need to find scalars a, b, c, and d such that b1 = ac1 + bc2 and b2 = cc1 + dc2. We can write this as a system of linear equations:

a2 + b3 = 1

a3 + b4 = 2

c2 + d3 = 1

c3 + d4 = 2

Solving this system gives a = -1/5, b = 6/5, c = 2/5, and d = -1/5. Therefore, we have:

b1 = (-1/5)*c1 + (6/5)*c2

b2 = (2/5)*c1 - (1/5)*c2

Thus, the change-of-coordinates matrix from B to C is:

[ -1/5 2/5 ]

[ 6/5 -1/5 ]

To find the change-of-coordinates matrix from C to B, we need to express the basis vectors of C in terms of the basis vectors of B and form the resulting matrix. This can be done by inverting the matrix we found earlier:

[ -1/5 2/5 ]

[ 6/5 -1/5 ]

To invert this matrix, we first need to find its determinant:

det([ -1/5 2/5 ]

[ 6/5 -1/5 ]) = (-1/5)(-1/5) - (2/5)(6/5) = -26/25

Now we can find the inverse:

[ -1/5 2/5 ] [ 1 2 ]

[ 6/5 -1/5 ] * [ 1 1 ] = [ 7/5 -2/5 ]

[ -2 1 ]

Therefore, the change-of-coordinates matrix from C to B is:

[ 7/5 -2/5 ]

[-2 1 ]

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